Minimal functional bases for elasticity tensor symmetry classes

Rodrigue Desmorat (1) , N Auffray (2) , B Desmorat (3) , M Olive (1) , Boris Kolev (1)

1 LMT - Laboratoire de mécanique et technologie
2 MSME - Laboratoire Modélisation et Simulation Multi-Echelle
3 DALEMBERT - Institut Jean Le Rond d'Alembert

Functional bases, synonymous with separating sets, are usually formulated for an entire vector space, such as the space Ela of elasticity tensors. We propose here to define functional bases limited to symmetry strata, i.e. sets of tensors of the same symmetry class. We provide such lowcardinal minimal bases for tetragonal, trigonal, cubic or transversely isotropic symmetry strata of the elasticity tensor.

Mots clés: Anisotropy; Covariants; Invariant theory; Symmetry classes

Domaines: Mécanique des matériaux [physics.class-ph]; Théorie des représentations [math.RT]

Rodrigue Desmorat, N Auffray, B Desmorat, M Olive, Boris Kolev. Minimal functional bases for elasticity tensor symmetry classes. Journal of Elasticity, 2022, ⟨10.1007/s10659-021-09872-2⟩. ⟨hal-03241501v2⟩